The period matrix of a smooth complex projective variety encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with high precision of the entries of the period matrix allow to recover some algebraic invariants of the variety, such as the Néron-Severi group in the case of surfaces. In this talk, we will see a method relying on the computation of an effective description of the homology for obtaining such numerical approximations of periods of algebraic varieties, and showcase implementations and applications, in particular to computation of the Picard rank of certain K3 surfaces related to Feynman diagrams.

In an AdS compactification the no-scale-separation conjecture states that the AdS scale cannot be parametrically separated from the KK scale of the internal manifold. This calls into question the validity of the effective lower-dimensional theory whilst also making holographic duals more complicated: obtaining a dense spectrum of low-dimension operators which are strongly mixed. This also poses problems for constructing de-Sitter vacua. 
I will discuss the papers Holography vs Scale Separation, Holographic Constraints on the String Landscape and A Holographic Constraint on Scale Separation which use holography to find constraints on scale separation, with the latter two papers focussing DGKT.